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Related Experiment Video

Updated: Jul 6, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Equation-free implementation of statistical moment closures.

Francis J Alexander¹, Gregory Johnson, Gregory L Eyink

¹Los Alamos National Laboratory, PO Box 1663, Los Alamos, New Mexico 87545, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 21, 2008

Summary

This study introduces a numerical method for statistical moment closures in complex nonlinear systems. The equation-free approach offers computational benefits for modeling systems without scale separation.

Related Experiment Videos

Last Updated: Jul 6, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

Computational Physics
Applied Mathematics
Nonlinear Dynamics

Background:

Modeling complex, large-scale nonlinear systems often requires statistical moment closures.
Existing methods can be computationally expensive or lack generality.
Equation-free methods offer a promising avenue for integrating closure dynamics.

Purpose of the Study:

To present a general numerical scheme for implementing statistical moment closures.
To demonstrate the practical application of equation-free methods for closure dynamics.
To explore computational advantages of numerical closure approaches.

Main Methods:

Developing a general numerical scheme for statistical moment closures.
Utilizing equation-free methods to numerically integrate closure dynamics.
Applying the approach to implement entropy-based Eyink-Levermore closures.

Main Results:

The proposed scheme enables practical implementation of closures even when equations are not in closed form.
The numerical closure approach offers significant computational advantages (fewer degrees of freedom, less stiffness).
Demonstrated successful application on a nonlinear stochastic partial differential equation.

Conclusions:

The equation-free numerical closure approach is broadly applicable to complex nonlinear systems, including strongly coupled and non-separable scale systems.
This method provides a computationally efficient alternative for modeling challenging systems.
The approach is validated through implementation on a nonlinear stochastic partial differential equation.